This article is cited in 9 papers

Characterization of the function spaces associated with weighted Sobolev spaces of the first order on the real line

D. V. Prokhorov^a, V. D. Stepanov^ab, E. P. Ushakova<sup>c

a</sup> Computing Centre of the Far Eastern Branch of Russian Academy of Sciences, Khabarovsk
^b Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
^c V. A. Trapeznikov Institute of Control Sciences of Russian Academy of Sciences, Moscow

Abstract: A brief survey of results on the characterization of the spaces associated with given classes of function spaces is presented. It is shown that the situation differs in general for ideal and non-ideal spaces. In the second case the notion of associated space splits into two. In the main body of the text a complete description is given of the function spaces associated with weighted Sobolev spaces of the first order on the real line.
Bibliography: 54 titles.

Keywords: function spaces, associated spaces, duality principle, weighted Sobolev spaces, Oinarov–Otelbaev construction, Hardy–Steklov integral operators.

UDC: 517.51

MSC: Primary 46E35; Secondary 46E30

Received: 28.12.2018
Revised: 30.09.2019

DOI: 10.4213/rm9873

 English version: Russian Mathematical Surveys, 2019, 74:6, 1075–1115

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